Objectives This paper seeks to study the free vibration characteristics of a cylindrical shell with T-shape ring stiffeners and bulkheads under different boundary conditions based on the Rayleigh−Ritz method.

Methods The classical Kirchhoff−Love shell theory and thin plate theory are used to establish a mathematical and physical model of the cylindrical shell and bulkheads. Using the Euler−Bernoulli beam theory, the T-shape ring stiffeners is regarded as a discrete element and the mathematical model is established by coordinate transformation through the relationship between its cross-section centroid and the displacement angle of the mid-surface of the shell. Modified Fourier series are selected as displacement penalty functions to integrate the displacement expression of the cylinder, plate, and T-shape ring stiffeners. The penalty functions are introduced to change the spring stiffness to simulate the continuous conditions between the bulkhead shells and the boundary conditions at both ends. The governing equations for the vibration of the coupled structure are obtained by means of energy functions.

Results The convergence, accuracy, and reliability of the proposed method are verified through a comparison with the numerical method results.

Conclusion This paper shows that the number and position of the T-shape ring stiffeners and bulkheads are closely related to the natural vibration characteristics of the coupled structure, providing certain references for engineering design and applications.